Ordinary Calabi-Yau-3 Crystals

Abstract

We show that crystals with the properties of crystalline cohomology of ordinary Calabi-Yau threefolds in characteristic p > 0, exhibit a remarkable similarity with the well known structure on the cohomology of complex Calabi-Yau threefolds near a boundary point of the moduli space with maximal unipotent local monodromy. In particular, there are canonical coordinates and an analogue of the prepotential of the Yukawa coupling. Moreover in Formulas (2.25) and (2.29) we show p-adic analogues of the integrality properties for the canonical coordinates and the prepotential of the Yukawa coupling, which have been observed in the examples of Mirror Symmetry. http://www.arxiv.org/abs/math.AG/0212061